Wednesday, July 25, 2012

NFL Statistical Analysis - Points Scored Standard Deviation

In recent articles I have discussed many indicators that can be used for future projections, including my Leading Indicators article and the pair of Turnover Analysis posted recently.Today let’s focus on points scored, and use one statistical analysis to project what a team’s performance may look like in 2012.

For this analysis we will use one observable metric, points scored, and examine a team’s YOY jump vs. their 10/11/12 year standard deviation in an attempt to identify squads that performed better or worse than their standard deviation, which is often a very solid indicator of their performance in the following season.Here is the data, all 32 NFL teams, and their points scored for each season going back to 1996:

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

ARI

18.8

17.7

20.3

15.3

13.1

18.4

16.4

13.9

17.8

19.4

19.6

25.3

26.7

23.4

18.1

19.7

ATL

19.3

20.0

27.6

17.8

15.8

18.2

25.1

18.7

21.3

21.9

18.3

16.2

24.4

22.7

25.9

25.1

BAL

23.2

20.4

16.8

20.3

20.8

18.9

19.8

25.3

19.8

16.6

22.1

17.2

24.1

24.4

22.3

23.6

BUF

19.9

15.9

25.0

20.0

19.7

16.6

23.7

15.3

24.7

16.9

18.8

15.8

21.0

16.1

17.8

23.3

CAR

22.9

16.6

21.0

26.3

19.4

15.8

16.1

20.1

22.2

24.4

16.9

16.8

25.9

19.7

12.3

25.4

CHI

17.7

16.4

17.3

17.0

13.5

21.1

17.6

17.7

14.4

16.3

26.7

20.9

23.4

20.4

20.9

22.1

CIN

23.3

22.2

16.8

17.7

11.6

14.1

17.4

21.6

23.2

26.3

23.3

23.8

12.8

19.1

20.1

21.5

CLE

13.6

10.1

17.8

21.5

15.9

17.3

14.5

14.9

25.1

14.5

15.3

17.1

13.6

DAL

17.9

19.0

23.8

22.0

18.4

15.4

13.6

18.1

18.3

20.3

26.6

28.4

22.6

22.6

24.6

23.1

DEN

24.4

29.5

31.3

19.6

20.3

21.3

24.5

23.8

23.8

24.7

19.9

20.0

23.1

20.4

21.5

19.3

DET

18.9

23.7

19.1

20.1

19.2

16.9

19.1

16.9

18.5

14.9

19.1

21.6

16.8

16.4

22.6

29.4

GB

28.5

26.4

25.5

22.3

22.1

24.4

24.9

27.6

26.5

18.6

18.4

27.2

26.2

28.8

24.3

35.0

HOU

13.3

15.8

19.3

16.3

16.7

23.7

22.9

24.3

24.4

23.8

IND

19.8

19.6

19.4

26.4

26.8

25.8

21.8

27.9

32.6

27.4

26.7

28.1

23.6

26.0

27.2

15.2

JAC

20.3

24.6

24.5

24.8

22.9

18.4

20.5

17.3

16.3

22.6

23.2

25.3

18.9

18.1

22.1

15.2

KC

18.6

23.4

20.4

24.4

22.2

20.0

29.2

30.3

30.2

25.3

20.7

14.1

18.2

18.4

22.9

13.3

MIA

21.2

21.2

20.1

20.4

20.2

21.5

23.6

19.4

17.0

19.8

16.3

16.7

21.6

22.5

17.1

20.6

MIN

18.6

22.1

34.8

24.9

24.8

18.1

24.4

26.0

25.3

19.1

17.4

22.8

23.7

29.6

17.3

21.3

NE

26.1

23.1

21.1

18.7

17.3

23.2

23.8

21.8

27.3

23.7

24.1

36.8

25.6

26.7

32.4

32.1

NO

14.3

14.8

19.1

16.3

22.1

20.8

27.0

21.3

21.8

14.7

25.8

22.4

28.9

31.9

24.0

34.2

NYG

15.1

19.2

17.9

18.7

20.5

18.4

19.8

15.2

18.5

26.4

22.2

23.3

26.7

25.1

24.6

24.6

NYJ

17.4

21.8

26.0

19.3

20.1

19.3

22.4

17.7

20.8

15.0

19.8

16.8

25.3

21.8

22.9

23.6

OAK

21.3

20.3

18.0

24.4

29.9

24.9

28.1

16.9

20.0

18.1

10.5

17.7

16.4

12.3

25.6

22.4

PHI

22.7

19.8

10.1

17.0

21.9

21.4

26.1

23.4

24.1

19.4

24.9

21.0

26.0

26.8

27.4

24.8

PIT

21.5

23.3

16.4

19.8

20.1

22.0

24.4

18.8

23.3

24.3

22.1

24.6

21.7

23.0

23.4

20.3

SD

19.4

16.6

15.1

16.8

16.8

20.8

20.8

19.6

27.9

26.1

30.8

25.8

27.4

28.4

25.6

25.4

SF

24.9

23.4

29.9

18.4

24.3

25.6

22.9

24.0

16.2

14.9

18.6

13.7

21.2

19.8

19.1

23.8

SEA

19.8

22.8

23.3

21.1

20.0

18.8

22.2

25.3

23.2

27.6

20.9

24.6

18.4

17.5

19.4

20.1

STL

18.9

18.7

17.8

32.9

33.8

31.4

19.8

27.3

19.9

22.7

22.9

16.4

14.5

10.9

18.1

12.1

TB

13.8

18.7

19.6

16.9

24.3

20.3

21.6

18.8

18.8

18.8

13.2

20.9

22.6

15.3

21.3

17.9

TEN

21.6

20.8

20.6

24.5

21.6

21.0

22.9

27.2

21.5

18.7

20.3

18.8

23.4

22.1

22.3

20.3

WAS

22.8

20.4

19.9

27.7

17.6

16.0

19.2

17.9

15.0

21.1

19.2

20.9

16.6

16.6

18.9

18.0

If you are reading this and aren’t familiar with the term standard deviation, or are not sure how to calculate it, both of those questions are answered rather easily.Standard deviation by definition is a measurement that shows how much variation or dispersion exists amongst a group of numbers vs. the average of that same group.In NFL terms for this analysis, it measures the boundaries of expected growth or decline a team can expect year to year based on their past results.To calculate this number, simply input your data in any row or column, go to the end of either, and in that cell type STDEV(in the parentheses input each cell that has a data point you would like to include in the calculation).

Once you get your 3 standard deviation measurements (10, 11, 12 years), what we now want to do is multiply those by 2 as that will provide you a figure which is estimated to include 95% of all observations – multiplying by two essentially gives us a 95% chance a team’s points scored from one season to the next will fall within that # shown.

Once you have your 2x standard deviation figure for all 3 scenarios, we want to compare that figure to the absolute value – calculated in Excel by simply typing ABS(the cell you are trying to get the absolute value of inside these parenthesis) – of the YOY change for the most recent two years – and if that absolute value figure falls outside the 2x standard deviation figure, that is either a red or green flag that a correction is likely to occur the following season.Red flag teams, or team’s that appear to be headed for a decrease in points scored will show a positive value in the YOY growth column prior to getting the absolute value of that number; green flag teams that are due to increase their points scored the next season will have a negative number in their YOY growth prior to getting the absolute value of that same number – intuitively, that makes sense, right?A team that had a big decline YOY compared to their Standard Deviation would in fact be expected to rise, and get within the bounds of the 95% confidence interval as soon as possible – the next season.

Now that I have laid out the process, I will do one team from the data above so as to walk you through your own excel file, and confirm you are performing all the calculations correctly and reaching the same conclusions.Let’s look at ARI, since they are right at the top, using data heading into the 2012 season:

Conclusion: 1.6 is well within the Standard Deviation x 2 ranges that hover around 8.0, so this analysis would not suggest any movement to ARI’s points scored in 2012.

Now that we all know what we are trying to analyze here, and how to perform the analysis, let me show you the back testing I have done for this article on this phenomenon.I have used the data above to go back 5 seasons to see how team’s performed when the data suggested a move one way or another.And here are the results:

Green

Red

TOTAL

2011

2-0

2-1

4-1

2010

1-0

-

1-0

2009

3-2

3-2

6-4

2008

-

3-1

3-1

2007

1-0

3-0

4-0

TOTAL

7-2

11-4

18-6

%

77.8%

73.3%

75.0%

The back testing suggests this is another solid statistical angle to use when attempting to project points scored – which ultimately leads to wins, and covers.I have back tested this data further than just the last 5 seasons with similar results, just slightly weaker in terms of %.

So now the big question obviously is which teams fit either scenario heading into 2012?Without further ado, here are the projected teams to rise or fall in points scored this season:

Green Light:IND, JAC.I think it’s a pretty solid prediction to assume both these teams will improve their points scored in the coming season.IND was a disaster last year under center with the Peyton Manning injury, while still facing a tough schedule because of a first place finish in 2010.JAC, like IND, had big time struggles at the QB position, but that should improve at least modestly with Gabbert entering his 2nd season, along with the addition of Justin Blackmon on the outside.Do not get me wrong, as mentioned in another article I am not bullish on Gabbert being an NFL caliber signal caller, but I think a certain level of improvement is likely based on the experience factor, and a key addition to his WR corps.

Red Flag: CAR, GB.

Green Bay Packers: once again another metric suggests GB will drop off from last season’s magical 15-1 regular season.A correction is expected to occur in their TOM, using both YOY and YOY YOY comparisons, along with the points scored standard deviation model.Expect GB to drop from 15 wins.

Carolina Panthers: we have a bit of a discrepancy with the Panthers as the points scored standard deviation model suggests a downward adjustment in points scored is likely, but in my Leading Indicators article posted on May 11th CAR had two of the three measurements pointing towards an improvement record wise: yards per play metric projects CAR should add more wins this year with similar offensive production as they were the only sub .500 team amongst the top 12 in yards per play, while the first downs per game metric also suggests an improvement to wins as they were the only sub .500 team amongst the top 13 in this metric.There is really little reason to assume either of those metrics will drastically move the other way, downward, as Cam Newton set numerous rookie passing records last season and he will be entering just his 2nd season – like any young QB, especially of the quality of Newton, better play is expected over their initial 3-4 seasons before settling into a grove.Because of that, CAR added to the defensive side of the ball in Rd1 with the selection of LB Luke Kuechly, and had a lot of missed games last year from defensive starters due to injury – so really there is no reason their defense won’t improve, the offense could potentially drop some from a points perspective, all leading to more wins and all three indicators being accurate.

To summarize, the points scored metric is obviously solid to use when projecting future team success.Using this type of analysis that involves some statistical measurements can add value – I have shown that over the last 5 seasons, 75% of the teams that were projected to trend upward or downward in points scored based on their standard deviation revert the way we project.

Take this piece of analysis, along with others I have discussed already and will discuss in the future before the season begins, and others you work on yourself, and start piecing together your jigsaw puzzle for the upcoming season.Having ideas before the season about certain teams and the chances their play improves or worsens compared to last year can really help your handicapping efforts.

Next week I will be back with another 10-12 NCAAF team preview capsules.I have now completed 62 of 68 BCS conference team previews, and will commence working on the remaining ~42 non-AQ teams I have not studied to this point in the coming weeks.

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